Obituaries often fail to include the date of death and instead just state that the person died 'last Tuesday.' Unfortunately, it's often difficult for genealogists to determine what date 'last Tuesday' was.
The calendars displayed are modern (i.e., Gregorian or New Style) calendars as opposed to the Julian or Old Style calendars. In October of 1582 Pope Gregory XIII instituted a 'new and improved' calendar that replaced the older Julian calendar. It was quickly adopted in most Catholic countries, but the many Protestant and Orthodox countries continued to use the older Julian calendar for centuries. Russia, for instance, continued to use the Julian calendar until Feb 14, 1918.
In regards to American genealogy, England and her American colonies switched to the Gregorian calendar on Sept 14, 1752, so these calendars can be used by American genealogist from that time forward. (Hopefully I'll be implementing support for Julian calendars in the near future.)